Problem: Simplify the following expression: $\dfrac{66y}{33y^3}$ You can assume $y \neq 0$.
Answer: $ \dfrac{66y}{33y^3} = \dfrac{66}{33} \cdot \dfrac{y}{y^3} $ To simplify $\frac{66}{33}$ , find the greatest common factor (GCD) of $66$ and $33$ $66 = 2 \cdot 3 \cdot 11$ $33 = 3 \cdot 11$ $ \mbox{GCD}(66, 33) = 3 \cdot 11 = 33 $ $ \dfrac{66}{33} \cdot \dfrac{y}{y^3} = \dfrac{33 \cdot 2}{33 \cdot 1} \cdot \dfrac{y}{y^3} $ $\phantom{ \dfrac{66}{33} \cdot \dfrac{1}{3}} = 2 \cdot \dfrac{y}{y^3} $ $ \dfrac{y}{y^3} = \dfrac{y}{y \cdot y \cdot y} = \dfrac{1}{y^2} $ $ 2 \cdot \dfrac{1}{y^2} = \dfrac{2}{y^2} $